EngineeringFormulaEngineering Mechanics
Acceleration Calculator
Calculate linear or centripetal acceleration, or solve for initial velocity, final velocity, time, or radius from the active kinematics formula.
Acceleration measures how quickly velocity changes. This calculator covers two common mechanics cases: one-dimensional linear motion using a = (v - u) / t, plus the constant-acceleration relation v = u + a t for solving a missing initial velocity, final velocity, or time, and uniform circular motion using centripetal acceleration a = v² / r. Choose the mode that matches your problem, then enter the known values to solve for the missing quantity.
u · Velocity at the start of the chosen time interval.
v · Velocity at the end of the chosen time interval.
t · Elapsed time over which the linear velocity change occurs.
Linear mode supports signed values along one chosen axis. Solving acceleration from u, v, and t gives average acceleration; solving for u, v, or t assumes acceleration is constant over the interval.
Solution
Enter the required values to calculate acceleration.
a = (v - u) / t
Formula Sheet
- aAcceleration
- uInitial Velocity
- vFinal Velocity or Tangential Speed
- tTime Interval
- rRadius
Variables & Units
| Symbol | Variable | Description | Common Units |
|---|---|---|---|
| a | Acceleration | Rate of change of velocity in linear motion, or inward radial acceleration magnitude in uniform circular motion. | m/s², ft/s², g |
| u | Initial Velocity | Velocity at the start of the chosen time interval in linear motion. | m/s, km/h, mph, ft/s |
| v | Final Velocity or Tangential Speed | Ending velocity in linear mode, or speed magnitude along the circular path in centripetal mode. | m/s, km/h, mph, ft/s |
| t | Time Interval | Elapsed time over which the linear velocity change occurs. | ms, s, min, h |
| r | Radius | Radius of the circular path measured from the center of rotation to the moving object. | mm, cm, m, in, ft |
How to Use This Calculator
- 01Choose the motion type first. Use Linear for one-dimensional velocity-change problems. In Linear mode, solving acceleration from u, v, and t gives average acceleration, while solving for u, v, or t assumes acceleration stays constant over the interval.
- 02Select which variable to solve for. The calculator will show only the inputs required for that form of the equation.
- 03For vehicle or machine problems, convert speeds to the same units before comparing results. A mph-to-ft/s or km/h-to-m/s mismatch is one of the easiest ways to get a misleading acceleration.
- 04Enter the known values with their units, then select Calculate to see the result in base SI units, the active formula, and the substitution.
- 05In Linear mode, signed velocities and accelerations are allowed for a one-axis sign convention. In Centripetal mode, the tool reports magnitudes only, so enter positive speed and radius values.
How the Formula Works
For linear motion, average acceleration is the change in velocity divided by the time interval: a = (v - u) / t. When acceleration is constant, the same relationship rearranges to v = u + a t, so you can solve not only for acceleration, but also for initial velocity, final velocity, or time.
For uniform circular motion, speed may stay constant while direction changes continuously. That directional change produces centripetal acceleration with magnitude a = v² / r, directed toward the center of the circular path. Doubling the speed quadruples centripetal acceleration, while doubling the radius cuts it in half.
Worked Example 01
Linear acceleration from a speed change
Known
- Initial Velocity (u): 0 m/s
- Final Velocity (v): 20 m/s
- Time (t): 5 s
Formula
a = (v - u) / t
Substitution
a = (20 - 0) / 5
Result
a = 4 m/s²
If an object goes from rest to 20 m/s in 5 s, its average acceleration over that interval is 4 m/s².
Worked Example 02
Solving for time in constant-acceleration motion
Known
- Initial Velocity (u): 5 m/s
- Final Velocity (v): 25 m/s
- Acceleration (a): 2 m/s²
Formula
t = (v - u) / a
Substitution
t = (25 - 5) / 2
Result
t = 10 s
At a constant 2 m/s² acceleration, it takes 10 s to increase speed from 5 m/s to 25 m/s.
Worked Example 03
Centripetal acceleration of a car rounding a curve
Known
- Tangential Speed (v): 25 m/s
- Radius (r): 500 m
Formula
a = v² / r
Substitution
a = 25² / 500
Result
a = 1.25 m/s²
A car taking a 500 m radius curve at 25 m/s experiences 1.25 m/s² of inward centripetal acceleration.
Worked Example 04
Solving for speed from centripetal acceleration and radius
Known
- Centripetal Acceleration (a): 8 m/s²
- Radius (r): 50 m
Formula
v = √(a r)
Substitution
v = √(8 × 50)
Result
v = 20 m/s
A body moving in a 50 m radius circle must travel at 20 m/s to have a centripetal acceleration of 8 m/s².
Applications
- 01Introductory kinematics and dynamics homework problems
- 02Estimating vehicle, machine, or test-rig acceleration from speed change over time
- 03Checking circular-motion loads and ride dynamics from speed and turning radius
Assumptions
- 01Linear mode applies one-dimensional average acceleration and the constant-acceleration relation v = u + a t.
- 02Centripetal mode assumes uniform circular motion and reports acceleration magnitude only.
- 03All calculations are deterministic and use internally converted SI base units.
Where This Model Stops
- 01Linear mode does not model acceleration that changes significantly over the time interval.
- 02Centripetal mode does not include tangential acceleration, nonuniform rotation, or full vector decomposition in two or three dimensions.
- 03Does not include friction, drag, grade, traction limits, jerk, drivetrain limits, or load-transfer effects.
References
- [1]3.1 Acceleration
OpenStax Physics
Defines average acceleration as the change in velocity over the change in time.
- [2]4.4 Uniform and Nonuniform Circular Motion
OpenStax University Physics Volume 1
States the centripetal-acceleration magnitude a_c = v²/r and explains its inward direction.
Frequently Asked Questions
Is negative acceleration the same as deceleration?
Not always. A negative acceleration just means the acceleration points in the negative direction of your chosen axis. Whether the object is slowing down depends on the relationship between the signs of velocity and acceleration.
Can an object accelerate if its speed stays constant?
Yes. In uniform circular motion the speed magnitude can remain constant while the velocity direction changes continuously, which creates centripetal acceleration toward the center of the path.
How is this different from the Force Calculator?
The Force Calculator uses Newton's second law a = F/m from a known net force. This Acceleration Calculator focuses on kinematics: velocity change over time and circular-motion acceleration from speed and radius.
How is this different from the Centripetal Force Calculator?
This page can solve the circular-motion acceleration a = v²/r by itself. The Centripetal Force Calculator goes one step further and multiplies that acceleration by mass to find the inward net force.